For the following data, construct a fraction defective chart by using 3 sigma. Is the process under control? NO. OF DEFECTIVES GROUP SAMPLE SIZE 1 160 22 2 160 27 3 250 27 4 250 22 5 160 17 6 400 32 7 250 22 8 250 22 9. 160 22 10 160 17 11 400 37 12 400 27
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- Using samples of 200 credit card statements, an auditor found the following: Sample 1 2 3 4 Number with errors 4 2 5 9 a. Determine the fraction defective in each sample. b. If the true fraction defective for this process is unknown, what is your estimate of it? c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? d. What control limits would give an alpha risk of .03 for this process? Page 457 e. What alpha risk would control limits of .047 and .003 provide? f. Using control limits of .047 and .003, is the process in control? g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control? Can you show me the steps and formulas using excelUsing samples of 200 credit card statements, an auditor found the following:Sample 1 2 3 4Number with errors 4 2 5 9a. Determine the fraction defective in each sample.b. If the true fraction defective for this process is unknown, what is your estimate of it?c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size?d. What control limits would give an alpha risk of .03 for this process?e. What alpha risk would control limits of .047 and .003 provide?f. Using control limits of .047 and .003, is the process in control?g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What arethe values of the mean and standard deviation of the sampling distribution?h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using twosigma control limits. Is the process in control?Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 60.75 lb.; Average range R = 1.64 lb. a) For the given sample size, the control limits for 3-sigma x chart are: Upper Control Limit (UCLx) = nothing lb. (round your response to three decimal places).
- At Gleditsia Triacanthos Company, a certain manufactured part is deemed acceptable if its lengthis between 12.45 to 12.55 inches. The process is normally distributed with an average of 12.49inches and a standard deviation of 0.014 inches. A) Is the process capable of meeting specifications? B) Does the process meet specifications?4. Organic Grains LLC uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight. Based on a previously stable and in-control process, the control limits of the x- and R-charts are: UCLx = 5.35, LCLx = 4.93; UCLR = 0.894, LCLR = 0. Over the past few days, they have taken five random samples of four loaves each and have found the following: Net Weight Sample Loaf # 1 Loaf # 2 Loaf # 3 Loaf # 4 1 4.9 5.2 5.1 5.0 2 5.3 5.1 5.2 5.3 3 4.9 5.2 4.9 5.2 4 5.5 5.5 5.3 5.5 5 5.3 5.2 5.3 5.0 Part 2 Based on the x-chart, is one or more samples beyond the control limits? ▼ No Yes .The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control. Day Sample Size Defects 1 100 8 2 120 4 3 190 10 4 190 7 5 240 20 6 245 8 7 105 4 8 165 6 9 245 27 10 255 37 Find the UCL. Find the LCL. Is the process in control? Why/why not?
- Jamison Kovach Supply Company manufactures paper clips and other office products. Although inexpensive, paper clips have provided the firm with a high margin of profitability. Sample size is 50. Results are given for the last 10 samples. Sample 1 2 3 4 5 6 7 8 9 10Defectives 5 8 3 5 6 5 5 4 1 11 a) Establish the control limits to include of the random variation in defectives. UCLp = [ ? ] (enter your response as a number between 0 and 1, rounded to three decimal places). LCLp = [ ? ] (enter your response as a number between 0 and 1, rounded to three decimal places). c) If the sample size were 100 instead, how would your limits and conclusions change? UCLp = [ ? ] (enter your response as a number between 0 and 1, rounded to three decimal places). LCLp = [ ? ] (enter your response as a number between 0 and 1, rounded to three…A process filling small bottles with baby formula hasa target of 3 ounces ± 0.150 ounce. Two hundred bottles fromthe process were sampled. The results showed the averageamount of formula placed in the bottles to be 3.042 ounces. Thestandard deviation of the amounts was 0.034 ounce. Determinethe value of Cpk· Roughly what proportion of bottles meetthe specifications?A production manager at a Contour Manufacturing planthas inspected the number of defective plastic molds in 5 randomsamples of 20 observations each. Following are the number ofdefective molds found in each sample: Construct a 3-sigma control chart (z = 3) with this information
- For 100 consecutive days, a company making nutritional supplements has measured theamount of a protein the company puts into its protein bars. Each day, the company takesa sample of 6 protein bars. The average across all 600 bars was 31.232 grams. The standard deviation was 0.83291 gram. When constructing an X-bar chart, what would theupper control limit be?a. 30.2119b. 31.232c. 32.2521d. None of the aboveNgqabutho Ltd produces plastic bottles to customer’s order. The quality inspector randomly selectsfour bottles from the bottle machine and gathers the following data ( see image) 1. Assume that only these six samples are sufficient, and use the data to determine controllimits for an R (range)- and an X (mean) chart. ( 2. Suppose that the specification for the bottle neck diameter is 0.600 ± 0.050 and thepopulation standard deviation is 0.013 in. What are the process capability index and theprocess capability ratio?An inspector counted the number of defective monthly billing statements of a telephonecompany in each of 20 samples. Using the following information, construct a control chartthat will describe 99.74 percent of the chance variation in the process when the process is incontrol. Each sample contained 100 statements.Sample Number ofDefectivesSample Number ofDefectivesSample Number ofDefectivesSample Number ofDefectives1 7 6 11 11 8 16 102 10 7 10 12 12 17 83 12 8 18 13 9 18 124 4 9 13 14 10 19 105 9 10 10 15 16 20 21220
